Also, either of the sentences you've used are okay. 日本語 and 英語 in this context are not adjectives - this is why you have to use の to connect the two nouns in the first place. の always indicates a possessive, and in this case, it is "English's class" and "Japanese's class." Very odd in English, but perfectly okay in Japanese.

So, don't worry about all the rules of adjectival connection in this sentence.
英語と日本語のクラスがあります。
and
英語のクラスと日本語のクラスがあります。
are both fine just as they are.

Mukade wrote:日本語のクラス and 英語のクラス are correct.[...]の always indicates a possessive, and in this case, it is "English's class" and "Japanese's class." Very odd in English, but perfectly okay in Japanese.

Being Italian, this wouldn't have been a problem for me as in Italy we say exatcly as in Japan (e.g. "corso di Giapponese", where di is the italian equivalent for no particle).
The real problem for us Italians is the inversion of the order, as we don't have a genitive form like 's in English (so we actually can only say something like "class of Japanese" which is radically different from "Japanese no class").
So, amusingly enough, the best way for me to remember the correct order of the words around no in Japanese is through English genitive 's, which I'm already used to... LOL!